Kolam Tile Laboratory
STATUS · WORKING ON NOW
The question
What becomes visible when the sixteen four-bit tiles are treated at once as a construction problem, a graph and a labelled sliding puzzle?
Current focus
Developing the interactive laboratory and its companion explanations.
Latest update
The construction board, sliding puzzle and orbit challenge are available to explore.
Open the interactive laboratory
Why this project
Each of the sixteen four-bit words describes the openings of a square tile in the directions east, north, west and south. The local rule is simple: adjacent bits must match. A closed boundary adds another family of local constraints, while requiring one connected drawing introduces a genuinely global condition.
Setting aside the \(0000\) tile turns the same objects into a labelled 15-puzzle. The question changes from which boards are valid? to which valid boards can be joined by legal slides? This brings parity and orbit structure into the picture.
Project strands
Build
Arrange all sixteen tiles while the board reports edge mismatches, boundary leaks and disconnected components.
Move
Treat the zero tile as an empty square and examine what is preserved by every legal slide.
Explain
Connect the experiments to binary encodings, graph connectivity, enumeration and proof.
Next steps
- expand the orbit challenge and explanations of its invariant;
- add downloadable classroom material;
- record a video walkthrough with a full companion page;
- document computational experiments where they provide useful evidence.